This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.
  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

Table X. Unconverged parameters.

area

variable

year

user

species

Rhat

BSAI

Ro_ayu

41

1.281005

BSAI

Ro_ayu

10

1.278735

BSAI

Ro_ay

41

1.277741

BSAI

Ro_ay

10

1.277649

BSAI

Ro_ayu

39

1.265166

BSAI

Ro_ay

39

1.263068

BSAI

Ro_ayu

19

1.256013

BSAI

Ry_ayu

9

1.248368

BSAI

Ry_ay

9

1.247258

BSAI

Ro_ay

19

1.238976

BSAI

Ry_ayg

4

1.226727

BSAI

Ro_ayu

6

1.220982

BSAI

Ry_ayu

21

1.200189

BSAI

Ro_ayu

37

1.199695

BSAI

Ry_ay

21

1.199492

BSAI

Ro_ayu

40

1.199246

BSAI

Ro_ay

40

1.194846

BSAI

Ro_ay

37

1.190253

BSAI

Ro_ay

6

1.189699

BSAI

Ro_ayu

32

1.187795

BSAI

Ro_ay

32

1.182881

BSAI

Ho_ayu

18

1.180879

BSAI

Ro_ayu

17

1.179150

BSAI

Ro_ay

17

1.173635

BSAI

Ro_ayg

1

1.172936

BSAI

Ho_ayu

7

1.169968

BSAI

Ho_ay

18

1.168489

BSAI

Ro_ayu

21

1.161129

BSAI

Ro_ayu

26

1.159803

BSAI

Ro_ay

21

1.158398

BSAI

Ho_ay

7

1.156235

BSAI

Ro_ay

26

1.152800

BSAI

Ry_ayg

8

1.147736

BSAI

Ro_ayg

19

1.147332

BSAI

Ro_ayg

9

1.142381

BSAI

Hb_ayg

8

1.141509

BSAI

H_ayg

8

1.137567

BSAI

Ho_ayg

8

1.137180

BSAI

Hp_ayg

8

1.137145

BSAI

Rb_ayg

8

1.134564

BSAI

Rp_ayg

8

1.132561

BSAI

R_ayg

8

1.131972

BSAI

Hy_ayg

16

1.130224

BSAI

Ro_ayu

15

1.129714

BSAI

Ro_ayu

44

1.129612

BSAI

Hy_ayu

7

1.125648

BSAI

Ro_ayu

7

1.124421

BSAI

Ro_ayu

1

1.123691

BSAI

Ro_ay

15

1.123585

BSAI

Hy_ay

7

1.120126

BSAI

Ro_ay

7

1.117066

CI

tau_beta1_black

1.270554

CI

mu_beta1_black

1.203082

CI

Ro_ayg

12

1.181868

CI

Ro_ayg

5

1.179248

CI

mu_beta1_pH

1

1.160985

CI

Ry_ayg

8

1.151294

CI

Ro_ayg

10

1.119193

CSEO

Rs_ayu

4

1.144708

CSEO

pH

47

2

2

1.116425

EWYKT

beta3_slope

27.986344

EWYKT

Hs_ayg

46

6.787981

EWYKT

Hs_ay

46

6.550558

EWYKT

p_slope

46

1

6.356931

EWYKT

Hs_ayg

45

5.363428

EWYKT

Hs_ay

45

5.341884

EWYKT

Ts_ayg

46

5.095012

EWYKT

Hs_ayg

47

4.698547

EWYKT

beta0_slope

4.601195

EWYKT

p_slope

45

1

4.588331

EWYKT

Ts_ay

46

4.564390

EWYKT

Hs_ay

47

4.542947

EWYKT

p_slope

47

1

4.116543

EWYKT

Ts_ayg

45

4.071585

EWYKT

Ts_ayg

47

4.034757

EWYKT

Ts_ay

47

4.009073

EWYKT

Ts_ay

45

3.874351

EWYKT

Hdnye_ayg

46

3.722796

EWYKT

Hd_ayg

46

3.681418

EWYKT

p_pelagic

46

1

3.646374

EWYKT

Tdnye_ayg

46

3.631831

EWYKT

Hdnye_ayg

45

3.231054

EWYKT

Hs_ayg

44

3.230052

EWYKT

Tdnye_ayg

45

3.219167

EWYKT

Hd_ayg

45

3.213788

EWYKT

p_pelagic

45

1

3.193084

EWYKT

Tdnye_ayg

47

3.085634

EWYKT

Hs_ay

44

3.073439

EWYKT

Ts_ayg

44

2.953753

EWYKT

p_slope

44

1

2.870734

EWYKT

Ts_ay

44

2.842458

EWYKT

Hdnye_ayg

47

2.773585

EWYKT

Hd_ayg

47

2.751942

EWYKT

Bdnye_ayg

45

2.740327

EWYKT

p_pelagic

47

1

2.735791

EWYKT

Bdnye_ayg

46

2.686205

EWYKT

Tdnye_ayg

44

2.402935

EWYKT

Bdnye_ayg

47

2.394723

EWYKT

Ts_ay

30

2.297194

EWYKT

Hs_ay

30

2.237986

EWYKT

Hdnye_ay

45

2.195511

EWYKT

Ts_ay

32

2.194870

EWYKT

Ts_ayg

30

2.185127

EWYKT

Hdnye_ayg

44

2.181073

EWYKT

Hd_ay

45

2.175585

EWYKT

Hd_ayg

44

2.164704

EWYKT

Hs_ay

32

2.153709

EWYKT

p_pelagic

44

1

2.144653

EWYKT

Bdnye_ayg

44

2.141971

EWYKT

p_slope

30

1

2.135554

EWYKT

Hs_ayg

30

2.133519

EWYKT

pr_slope

46

1

2.132335

EWYKT

Rs_ayg

46

2.130536

EWYKT

Ts_ayg

32

2.110759

EWYKT

pr_slope

47

1

2.107066

EWYKT

Rs_ayg

47

2.103937

EWYKT

pr_slope

45

1

2.098115

EWYKT

Rs_ayg

45

2.092169

EWYKT

Rs_ay

47

2.079386

EWYKT

Hs_ayg

32

2.072286

EWYKT

p_slope

32

1

2.065935

EWYKT

Rs_ay

45

2.053093

EWYKT

Ts_ay

31

2.028765

EWYKT

Rdnye_ayg

46

2.016917

EWYKT

Rdnye_ayg

45

2.008873

EWYKT

Ts_ay

33

1.993373

EWYKT

Rd_ayg

46

1.989831

EWYKT

Rdnye_ayg

47

1.983454

EWYKT

Rd_ayg

45

1.976444

EWYKT

Hs_ay

31

1.974080

EWYKT

Hs_ay

33

1.967800

EWYKT

Rd_ayg

47

1.949850

EWYKT

Ts_ayg

31

1.949552

EWYKT

Rs_ay

46

1.949330

EWYKT

p_slope

47

2

1.922263

EWYKT

Hs_ayg

31

1.901842

EWYKT

p_slope

31

1

1.894714

EWYKT

Ts_ayg

33

1.887624

EWYKT

Hs_ayg

33

1.870377

EWYKT

p_slope

33

1

1.864251

EWYKT

Ts_ay

34

1.863737

EWYKT

p_slope

46

2

1.854517

EWYKT

pr_slope

30

1

1.842001

EWYKT

Hs_ay

34

1.840273

EWYKT

pr_slope

44

1

1.831246

EWYKT

pr_slope

32

1

1.828854

EWYKT

Rs_ayg

44

1.828004

EWYKT

p_slope

45

2

1.813777

EWYKT

Ts_ayg

34

1.794394

EWYKT

Rs_ay

44

1.786952

EWYKT

Hs_ayg

34

1.775628

EWYKT

p_slope

34

1

1.772239

EWYKT

pr_slope

31

1

1.751239

EWYKT

re_rslope

36

1

1.744385

EWYKT

Hdnye_ay

46

1.736667

EWYKT

Rdnye_ayg

44

1.721020

EWYKT

Rs_ayg

32

1.716923

EWYKT

Hd_ay

46

1.713292

EWYKT

Rs_ayg

30

1.712438

EWYKT

pr_slope

47

2

1.710017

EWYKT

Rd_ayg

44

1.707666

EWYKT

Ho_ayg

46

1.696604

EWYKT

pr_slope

33

1

1.692413

EWYKT

p_slope

23

1

1.674283

EWYKT

beta4_slope

1.673583

EWYKT

Ts_ay

27

1.672620

EWYKT

Ts_ay

23

1.671206

EWYKT

p_slope

11

1

1.666130

EWYKT

p_slope

26

1

1.663667

EWYKT

pr_slope

46

2

1.660031

EWYKT

Ts_ay

29

1.654341

EWYKT

p_slope

15

1

1.652042

EWYKT

Hs_ay

23

1.650528

EWYKT

p_slope

19

1

1.649365

EWYKT

p_slope

12

1

1.646750

EWYKT

Ts_ay

22

1.646324

EWYKT

p_slope

4

1

1.644123

EWYKT

p_slope

14

1

1.641229

EWYKT

Ts_ay

26

1.641142

EWYKT

p_slope

8

1

1.639996

EWYKT

p_slope

6

1

1.637675

EWYKT

Hs_ay

27

1.637247

EWYKT

p_slope

18

1

1.633533

EWYKT

p_slope

20

1

1.632564

EWYKT

Hs_ay

29

1.631003

EWYKT

Ts_ay

28

1.630785

EWYKT

Rs_ayg

31

1.626705

EWYKT

Hs_ay

26

1.624748

EWYKT

p_slope

9

1

1.623396

EWYKT

p_slope

44

2

1.622878

EWYKT

Ts_ayg

27

1.621762

EWYKT

Hs_ay

22

1.621420

EWYKT

Ts_ayg

22

1.619934

EWYKT

pr_slope

36

2

1.617846

EWYKT

p_slope

25

1

1.612728

EWYKT

pr_slope

37

2

1.610306

EWYKT

p_slope

21

1

1.610025

EWYKT

Hs_ay

28

1.609276

EWYKT

p_slope

16

1

1.609180

EWYKT

pr_slope

38

2

1.608310

EWYKT

Rs_ay

30

1.606048

EWYKT

p_slope

28

1

1.605464

EWYKT

p_slope

29

1

1.604914

EWYKT

p_slope

3

1

1.602766

EWYKT

pr_slope

41

2

1.601859

EWYKT

p_slope

22

1

1.601592

EWYKT

p_slope

27

1

1.601512

EWYKT

Hs_ayg

22

1.598754

EWYKT

p_slope

2

1

1.598088

EWYKT

p_slope

7

1

1.596274

EWYKT

pr_slope

40

2

1.595376

EWYKT

p_slope

10

1

1.595276

EWYKT

Ts_ayg

23

1.594437

EWYKT

p_slope

17

1

1.592249

EWYKT

Hs_ayg

27

1.589933

EWYKT

p_slope

24

1

1.589632

EWYKT

Ts_ayg

28

1.586512

EWYKT

pr_slope

16

1

1.584821

EWYKT

pr_slope

39

2

1.584376

EWYKT

pr_slope

42

2

1.583215

EWYKT

Ts_ayg

29

1.579424

EWYKT

Ts_ay

25

1.578755

EWYKT

Ts_ay

24

1.577728

EWYKT

Hs_ayg

23

1.576484

EWYKT

p_slope

13

1

1.576282

EWYKT

re_slope

32

1

1.575103

EWYKT

pr_slope

34

1

1.572568

EWYKT

pH

46

1

3

1.571542

EWYKT

p_slope

5

1

1.569522

EWYKT

pr_slope

45

2

1.569194

EWYKT

pr_slope

22

1

1.568346

EWYKT

Hs_ayg

28

1.567997

EWYKT

pr_slope

20

1

1.565399

EWYKT

Hs_ayg

29

1.559937

EWYKT

Hs_ay

24

1.558848

EWYKT

p_slope

38

2

1.558084

EWYKT

Hs_ay

25

1.557809

EWYKT

pr_slope

14

1

1.557472

EWYKT

Ts_ayg

26

1.554228

EWYKT

pr_slope

27

1

1.553662

EWYKT

p_slope

1

1

1.543743

EWYKT

pr_slope

17

1

1.542432

EWYKT

pr_slope

25

1

1.541728

EWYKT

Hs_ayg

26

1.540209

EWYKT

pr_slope

11

1

1.538869

EWYKT

pr_slope

5

1

1.536902

EWYKT

pr_slope

24

1

1.532746

EWYKT

pr_slope

26

1

1.531807

EWYKT

pr_slope

10

1

1.529690

EWYKT

pr_slope

15

1

1.526363

EWYKT

pr_slope

13

1

1.526201

EWYKT

pr_slope

2

1

1.522907

EWYKT

pr_slope

35

2

1.522442

EWYKT

pr_slope

3

1

1.519729

EWYKT

pr_slope

28

1

1.515363

EWYKT

p_slope

37

2

1.514378

EWYKT

pr_slope

29

1

1.514337

EWYKT

re_slope

30

1

1.513765

EWYKT

pr_slope

19

1

1.512677

EWYKT

pr_slope

18

1

1.512616

EWYKT

pr_slope

1

1

1.511741

EWYKT

pr_slope

9

1

1.510911

EWYKT

pr_slope

44

2

1.509495

EWYKT

pr_slope

7

1

1.507773

EWYKT

Ts_ayg

25

1.507680

EWYKT

p_slope

39

2

1.498802

EWYKT

p_slope

40

2

1.495889

EWYKT

pr_slope

21

1

1.495495

EWYKT

Ts_ayg

24

1.495028

EWYKT

Rs_ayg

33

1.494681

EWYKT

Hs_ayg

25

1.490001

EWYKT

pr_slope

23

1

1.482755

EWYKT

pr_slope

4

1

1.481423

EWYKT

Hs_ayg

24

1.479804

EWYKT

pr_slope

12

1

1.473566

EWYKT

Rs_ay

31

1.467404

EWYKT

pr_slope

6

1

1.463728

EWYKT

Rs_ayg

34

1.461425

EWYKT

pr_slope

8

1

1.451769

EWYKT

p_slope

36

2

1.449097

EWYKT

p_slope

42

2

1.447308

EWYKT

p_slope

41

2

1.446663

EWYKT

Hs_ayu

47

1.446231

EWYKT

p_slope

22

2

1.445091

EWYKT

re_rslope

42

1

1.438222

EWYKT

p_slope

6

2

1.434265

EWYKT

p_slope

15

2

1.430644

EWYKT

p_slope

5

2

1.425829

EWYKT

p_slope

23

2

1.423431

EWYKT

Hs_ayu

46

1.420723

EWYKT

p_slope

13

2

1.417290

EWYKT

p_slope

32

2

1.416833

EWYKT

p_slope

29

2

1.412971

EWYKT

Ts_ayu

42

1.407926

EWYKT

p_slope

1

2

1.407021

EWYKT

Ts_ayu

40

1.404039

EWYKT

p_slope

31

2

1.402161

EWYKT

p_slope

30

2

1.402010

EWYKT

p_slope

12

2

1.401568

EWYKT

p_slope

19

2

1.398706

EWYKT

p_slope

8

2

1.392071

EWYKT

p_slope

10

2

1.390872

EWYKT

p_slope

17

2

1.390806

EWYKT

p_slope

25

2

1.388630

EWYKT

Ts_ayu

39

1.388475

EWYKT

p_slope

4

2

1.387171

EWYKT

pr_slope

17

2

1.386270

EWYKT

pr_slope

25

2

1.385605

EWYKT

p_slope

2

2

1.384851

EWYKT

Rs_ay

32

1.384190

EWYKT

Ts_ay

11

1.383562

EWYKT

Ts_ayu

37

1.382884

EWYKT

p_slope

24

2

1.382108

EWYKT

Ts_ayu

36

1.380106

EWYKT

pr_slope

32

2

1.378771

EWYKT

Hs_ay

11

1.378378

EWYKT

Hs_ayu

40

1.378018

EWYKT

Ts_ayu

47

1.375935

EWYKT

p_slope

9

2

1.371640

EWYKT

p_slope

16

2

1.371395

EWYKT

pr_slope

27

2

1.370982

EWYKT

p_slope

33

2

1.370931

EWYKT

pr_slope

24

2

1.369601

EWYKT

pr_slope

15

2

1.369495

EWYKT

p_slope

14

2

1.369463

EWYKT

pr_slope

2

2

1.369353

EWYKT

pr_slope

5

2

1.369232

EWYKT

re_slope

45

1

1.368572

EWYKT

pr_slope

7

2

1.368370

EWYKT

Ts_ay

17

1.366532

EWYKT

p_slope

3

2

1.366198

EWYKT

pr_slope

31

2

1.365852

EWYKT

Hs_ayu

37

1.365161

EWYKT

p_slope

7

2

1.364981

EWYKT

p_slope

20

2

1.364977

EWYKT

re_slope

36

1

1.364846

EWYKT

pr_slope

1

2

1.364188

EWYKT

p_slope

21

2

1.363926

EWYKT

pr_slope

14

2

1.363875

EWYKT

p_slope

27

2

1.363635

EWYKT

pr_slope

16

2

1.363112

EWYKT

pr_slope

22

2

1.362505

EWYKT

pr_slope

29

2

1.362177

EWYKT

pr_slope

12

2

1.361667

EWYKT

pr_slope

4

2

1.361055

EWYKT

Ts_ay

19

1.360713

EWYKT

pr_slope

21

2

1.360526

EWYKT

Hs_ay

17

1.359632

EWYKT

p_slope

26

2

1.359026

EWYKT

Hs_ayu

36

1.358195

EWYKT

Ts_ayu

41

1.358117

EWYKT

pr_slope

19

2

1.357929

EWYKT

pr_slope

23

2

1.357585

EWYKT

p_slope

28

2

1.357459

EWYKT

pr_slope

13

2

1.354558

EWYKT

pr_slope

30

2

1.354436

EWYKT

Hs_ay

19

1.353616

EWYKT

p_slope

11

2

1.352729

EWYKT

pr_slope

18

2

1.352667

EWYKT

pr_slope

26

2

1.350004

EWYKT

pr_slope

10

2

1.349637

EWYKT

Ts_ay

8

1.348264

EWYKT

pr_slope

9

2

1.347501

EWYKT

Ts_ayg

11

1.347376

EWYKT

Hs_ayu

39

1.346414

EWYKT

Hs_ayu

42

1.345897

EWYKT

pr_slope

3

2

1.344799

EWYKT

p_slope

18

2

1.344666

EWYKT

Hs_ay

8

1.344375

EWYKT

Ts_ay

12

1.344195

EWYKT

Hs_ayg

11

1.342609

EWYKT

pr_slope

28

2

1.342174

EWYKT

Hs_ayu

45

1.342148

EWYKT

pr_slope

33

2

1.342026

EWYKT

Ts_ay

38

1.341436

EWYKT

Hs_ay

12

1.338720

EWYKT

Ts_ay

2

1.338018

EWYKT

Ts_ay

14

1.337383

EWYKT

pr_slope

6

2

1.336275

EWYKT

Hs_ay

2

1.334851

EWYKT

pr_slope

11

2

1.333604

EWYKT

pr_slope

8

2

1.332362

EWYKT

Ts_ay

4

1.331734

EWYKT

Hs_ay

14

1.331638

EWYKT

Hs_ay

38

1.331253

EWYKT

Ts_ayg

17

1.331032

EWYKT

Ts_ay

20

1.328607

EWYKT

Hs_ay

4

1.327152

EWYKT

Ts_ayg

19

1.327017

EWYKT

Hs_ayg

17

1.324556

EWYKT

Ts_ayu

38

1.324468

EWYKT

p_slope

35

2

1.322622

EWYKT

Hs_ay

20

1.321427

EWYKT

Hs_ayg

19

1.320848

EWYKT

Ts_ay

16

1.319743

EWYKT

Hs_ayu

41

1.319157

EWYKT

Ts_ay

5

1.318839

EWYKT

Rs_ay

33

1.317466

EWYKT

Hs_ayu

38

1.315323

EWYKT

pr_slope

20

2

1.315297

EWYKT

Ts_ayg

8

1.313973

EWYKT

Hs_ay

16

1.313910

EWYKT

Bdnye_ay

45

1.313770

EWYKT

Hs_ay

5

1.313681

EWYKT

Ts_ay

21

1.311925

EWYKT

Ts_ayg

12

1.311546

EWYKT

Ts_ay

15

1.311110

EWYKT

Hs_ayg

8

1.310297

EWYKT

Ts_ay

18

1.308665

EWYKT

Ts_ayg

14

1.306774

EWYKT

Hs_ayg

12

1.306587

EWYKT

Ts_ayg

2

1.305373

EWYKT

Hs_ay

21

1.305369

EWYKT

Hs_ay

15

1.305312

EWYKT

Tdnye_ay

45

1.304699

EWYKT

Hs_ay

18

1.303502

EWYKT

Hs_ayg

2

1.302561

EWYKT

Ts_ayg

4

1.302086

EWYKT

Hs_ayg

14

1.301992

EWYKT

Ts_ayg

20

1.297949

EWYKT

Hs_ayg

4

1.297678

EWYKT

Ts_ay

10

1.296988

EWYKT

Ts_ayg

16

1.296683

EWYKT

Ts_ayu

30

1.293413

EWYKT

Hs_ay

10

1.292988

EWYKT

Hs_ayg

20

1.291941

EWYKT

Ts_ay

7

1.291630

EWYKT

Hs_ayg

16

1.291493

EWYKT

Ts_ayg

5

1.291062

EWYKT

Ts_ayu

33

1.287973

EWYKT

Hs_ay

7

1.287953

EWYKT

Hs_ayg

5

1.286404

EWYKT

Ts_ayg

15

1.284209

EWYKT

Ts_ayg

18

1.283844

EWYKT

Ts_ayg

21

1.282353

EWYKT

Ts_ayu

32

1.280736

EWYKT

Hs_ayg

18

1.279740

EWYKT

Rs_ay

28

1.279683

EWYKT

Hs_ayg

15

1.279006

EWYKT

Ts_ayu

35

1.278198

EWYKT

Hdnye_ay

44

1.278119

EWYKT

Hs_ayg

21

1.277064

EWYKT

Rs_ay

37

1.276960

EWYKT

Rs_ay

40

1.275008

EWYKT

Hs_ayu

30

1.273553

EWYKT

Rs_ayu

14

1.272853

EWYKT

Rs_ayu

36

1.272614

EWYKT

Ts_ayg

10

1.272556

EWYKT

Hs_ayu

32

1.270147

EWYKT

Rs_ay

22

1.269724

EWYKT

Hs_ayg

10

1.268742

EWYKT

Hs_ayu

33

1.268093

EWYKT

Hd_ay

44

1.267839

EWYKT

Rs_ay

24

1.267396

EWYKT

Ts_ay

3

1.267219

EWYKT

Ts_ayg

7

1.266908

EWYKT

Ts_ayu

31

1.265956

EWYKT

Hs_ay

3

1.264095

EWYKT

Ts_ay

6

1.264046

EWYKT

Hs_ayg

7

1.263423

EWYKT

Hs_ay

6

1.261143

EWYKT

Hs_ayu

35

1.260594

EWYKT

p_slope

34

2

1.257831

EWYKT

Rs_ayg

28

1.257799

EWYKT

Ts_ayu

44

1.256687

EWYKT

Ts_ayu

22

1.255658

EWYKT

Rs_ay

39

1.254684

EWYKT

re_slope

47

2

1.253825

EWYKT

Rs_ayu

42

1.252494

EWYKT

Ts_ayu

45

1.249232

EWYKT

Ts_ayg

3

1.248270

EWYKT

Rs_ay

25

1.247521

EWYKT

Hs_ayu

31

1.246853

EWYKT

Rs_ay

29

1.245813

EWYKT

Hs_ayg

3

1.245321

EWYKT

Rs_ayg

24

1.245073

EWYKT

Rs_ayu

39

1.244774

EWYKT

Ts_ay

37

1.244450

EWYKT

Ts_ayg

6

1.243241

EWYKT

Ts_ayu

23

1.243209

EWYKT

Rs_ay

41

1.242917

EWYKT

Ts_ayu

27

1.241916

EWYKT

Hs_ayu

44

1.241383

EWYKT

Hs_ayg

6

1.240699

EWYKT

Ts_ayu

25

1.238608

EWYKT

Rs_ayu

37

1.238123

EWYKT

Ts_ayu

46

1.236419

EWYKT

Rs_ayu

23

1.235828

EWYKT

Rs_ayg

22

1.234962

EWYKT

Ts_ay

9

1.233373

EWYKT

Hs_ayu

25

1.233138

EWYKT

Rs_ayg

29

1.233008

EWYKT

Ts_ayu

15

1.232507

EWYKT

Hs_ay

9

1.232334

EWYKT

Hs_ay

37

1.232253

EWYKT

Hs_ayu

23

1.232080

EWYKT

Ho_ayg

47

1.231225

EWYKT

Rs_ay

23

1.230149

EWYKT

Bdnye_ay

44

1.228660

EWYKT

Hs_ayu

22

1.227680

EWYKT

Rs_ay

26

1.227604

EWYKT

Rs_ayu

41

1.227489

EWYKT

Rs_ayg

25

1.226263

EWYKT

Hs_ayu

27

1.226084

EWYKT

Ts_ay

13

1.225410

EWYKT

Rs_ay

27

1.225062

EWYKT

Ts_ayg

9

1.224503

EWYKT

Rs_ayu

40

1.223990

EWYKT

Hs_ay

13

1.223848

EWYKT

Hs_ayu

15

1.223565

EWYKT

Hs_ayg

9

1.223257

EWYKT

Tdnye_ay

44

1.222640

EWYKT

Rs_ayu

35

1.219523

EWYKT

Ts_ayu

24

1.218076

EWYKT

Rs_ayu

22

1.217853

EWYKT

Ts_ayu

29

1.217296

EWYKT

Ts_ayu

17

1.216291

EWYKT

pDSR_YE_ayg

46

1.215612

EWYKT

p_yellow

46

1

1.215612

EWYKT

Ts_ayu

28

1.215382

EWYKT

beta1_slope

1.215038

EWYKT

Rs_ayg

26

1.213489

EWYKT

Ts_ayg

13

1.212585

EWYKT

Ts_ayu

12

1.212203

EWYKT

Hs_ayu

24

1.211249

EWYKT

Hs_ayg

13

1.211244

EWYKT

Ts_ayu

5

1.211242

EWYKT

Hs_ayu

17

1.211079

EWYKT

Ts_ayu

20

1.210487

EWYKT

Ts_ay

1

1.208685

EWYKT

Hdnye_ay

47

1.208535

EWYKT

Hs_ayu

29

1.208176

EWYKT

Ts_ayu

8

1.208084

EWYKT

Rs_ay

14

1.207924

EWYKT

Rs_ay

19

1.207659

EWYKT

Hs_ay

1

1.207530

EWYKT

Hs_ayu

12

1.207518

EWYKT

Rs_ay

15

1.206799

EWYKT

Rs_ayg

27

1.206717

EWYKT

Rs_ayu

10

1.206259

EWYKT

Hs_ayu

5

1.205564

EWYKT

Ts_ayu

26

1.204582

EWYKT

Hs_ayu

8

1.203329

EWYKT

Rs_ayg

23

1.203117

EWYKT

Hs_ayu

20

1.202955

EWYKT

Rs_ayg

20

1.202250

EWYKT

Hs_ayu

28

1.201670

EWYKT

re_slope

34

1

1.200972

EWYKT

Hd_ay

47

1.200743

EWYKT

Rs_ay

20

1.199543

EWYKT

Ts_ayu

11

1.198840

EWYKT

Ts_ayu

10

1.198821

EWYKT

Rs_ayg

15

1.198479

EWYKT

Hs_ayu

26

1.197941

EWYKT

Rs_ayu

20

1.196888

EWYKT

Rs_ayu

5

1.196154

EWYKT

Ts_ayg

1

1.195495

EWYKT

Ts_ayu

7

1.195354

EWYKT

Ts_ayu

19

1.194643

EWYKT

Rs_ayu

32

1.194614

EWYKT

Hs_ayg

1

1.194436

EWYKT

Rs_ay

18

1.193913

EWYKT

Rs_ay

34

1.193898

EWYKT

Rs_ayg

19

1.193796

EWYKT

Hs_ayu

10

1.193540

EWYKT

Ts_ay

40

1.193269

EWYKT

Hs_ayu

11

1.193257

EWYKT

beta1_dsr

1.193167

EWYKT

Ts_ayu

21

1.191321

EWYKT

pr_slope

39

1

1.190668

EWYKT

Rs_ay

35

1.190194

EWYKT

Ts_ayu

18

1.190164

EWYKT

Ts_ayu

2

1.190018

EWYKT

Hs_ayu

7

1.189861

EWYKT

Ts_ayu

14

1.189003

EWYKT

Hs_ayu

19

1.188838

EWYKT

Ts_ayu

1

1.188703

EWYKT

pH

47

1

3

1.187625

EWYKT

Rs_ayg

9

1.187190

EWYKT

Rs_ay

17

1.186522

EWYKT

Hs_ayu

1

1.186364

EWYKT

Hs_ayu

14

1.186298

EWYKT

Hs_ayu

2

1.186230

EWYKT

re_slope

42

1

1.185181

EWYKT

Ts_ayu

4

1.185159

EWYKT

Hs_ayu

21

1.185056

EWYKT

Ts_ayu

9

1.184496

EWYKT

Hs_ayu

9

1.184099

EWYKT

Ts_ayu

13

1.183978

EWYKT

Hs_ayu

18

1.183895

EWYKT

Rs_ayg

17

1.183631

EWYKT

Rs_ay

9

1.183510

EWYKT

Rs_ay

8

1.183129

EWYKT

Hs_ayu

4

1.181531

EWYKT

Rs_ayg

18

1.181308

EWYKT

pDSR_YE_ay

46

1.181139

EWYKT

pr_slope

38

1

1.180788

EWYKT

Hs_ayu

13

1.180617

EWYKT

Ts_ayu

6

1.180229

EWYKT

Rs_ayg

8

1.180110

EWYKT

Ts_ayu

34

1.178991

EWYKT

Hs_ay

40

1.178744

EWYKT

Ts_ayu

3

1.178291

EWYKT

Ts_ayu

16

1.178288

EWYKT

Hs_ayu

6

1.176279

EWYKT

Rs_ay

21

1.176084

EWYKT

Hs_ayu

3

1.174656

EWYKT

pr_slope

37

1

1.174103

EWYKT

Hs_ayu

16

1.173714

EWYKT

Rs_ay

11

1.172749

EWYKT

Rs_ay

12

1.172449

EWYKT

Rs_ayg

5

1.170761

EWYKT

Ho_ayg

45

1.170629

EWYKT

Bdnye_ay

46

1.169585

EWYKT

Rs_ayg

10

1.169472

EWYKT

Ts_ay

39

1.168894

EWYKT

Rs_ayg

14

1.168587

EWYKT

Rs_ay

38

1.168312

EWYKT

pr_slope

34

2

1.167160

EWYKT

Hs_ayu

34

1.167121

EWYKT

Rs_ayu

33

1.166829

EWYKT

re_slope

44

1

1.166319

EWYKT

Rs_ayu

47

1.166234

EWYKT

Tdnye_ay

46

1.166077

EWYKT

Rs_ayu

19

1.166021

EWYKT

Rs_ayg

11

1.164872

EWYKT

Rs_ayu

45

1.164350

EWYKT

Rs_ayg

21

1.163899

EWYKT

beta5_rslope

1.163458

EWYKT

Rs_ay

5

1.163253

EWYKT

Rs_ayg

12

1.163129

EWYKT

Rs_ayg

40

1.162404

EWYKT

Bdnye_ay

47

1.162327

EWYKT

Ho_ay

46

1.161914

EWYKT

Rs_ayu

6

1.161024

EWYKT

pr_slope

40

1

1.160362

EWYKT

Tdnye_ay

47

1.159534

EWYKT

Rs_ay

10

1.158835

EWYKT

Rs_ayu

26

1.156782

EWYKT

Rs_ay

3

1.156459

EWYKT

beta0_yellow

1.156305

EWYKT

Rs_ayu

2

1.156293

EWYKT

Rs_ayg

3

1.155948

EWYKT

Rs_ay

7

1.155908

EWYKT

Hs_ay

39

1.155666

EWYKT

pr_slope

43

2

1.154290

EWYKT

Rs_ayg

7

1.152619

EWYKT

Rs_ayu

34

1.150479

EWYKT

Rs_ayg

39

1.150226

EWYKT

Rs_ay

2

1.149961

EWYKT

Rs_ayu

31

1.149033

EWYKT

Rs_ay

6

1.147365

EWYKT

Rs_ayg

4

1.147270

EWYKT

re_rslope

32

1

1.146769

EWYKT

Rs_ayg

38

1.146256

EWYKT

Rs_ay

16

1.144918

EWYKT

Rs_ay

4

1.144901

EWYKT

Rs_ayg

37

1.144502

EWYKT

Rs_ayu

29

1.142711

EWYKT

Rs_ayg

2

1.142516

EWYKT

Rs_ayu

44

1.142288

EWYKT

Rs_ayu

38

1.141160

EWYKT

Rs_ayg

6

1.140521

EWYKT

re_slope

31

1

1.140278

EWYKT

Rs_ay

42

1.140084

EWYKT

beta1_yellow

1.139341

EWYKT

Rs_ayu

30

1.138864

EWYKT

re_rslope

47

2

1.138606

EWYKT

Rs_ay

13

1.137677

EWYKT

Rs_ayg

16

1.136638

EWYKT

pr_slope

41

1

1.135045

EWYKT

Rs_ayg

41

1.134708

EWYKT

Rs_ayu

12

1.134061

EWYKT

re_rslope

46

1

1.133685

EWYKT

Rs_ayu

11

1.133637

EWYKT

Rs_ayu

8

1.133444

EWYKT

re_rslope

30

1

1.133270

EWYKT

Rs_ayu

24

1.133180

EWYKT

Rs_ayg

1

1.132847

EWYKT

Rs_ayg

13

1.132712

EWYKT

Rs_ay

1

1.132069

EWYKT

Rs_ayu

27

1.131579

EWYKT

pH

45

1

3

1.130954

EWYKT

pDSR_YE_ayg

45

1.130951

EWYKT

p_yellow

45

1

1.130951

EWYKT

Rs_ayu

28

1.130926

EWYKT

Rs_ay

36

1.130797

EWYKT

Rs_ayu

46

1.129731

EWYKT

pDSR_YE_ay

45

1.128664

EWYKT

Ro_ayu

10

1.128484

EWYKT

pH

47

2

2

1.128350

EWYKT

re_slope

33

1

1.128236

EWYKT

Rdnye_ayu

10

1.128097

EWYKT

Rs_ayu

25

1.126269

EWYKT

Rs_ayu

7

1.125991

EWYKT

Rs_ayu

9

1.121687

EWYKT

Rs_ayu

15

1.121355

EWYKT

Rs_ayu

18

1.121164

EWYKT

Rs_ayu

16

1.119996

EWYKT

Ts_ay

41

1.119713

EWYKT

Rs_ayu

3

1.117293

EWYKT

re_slope

46

2

1.116343

EWYKT

re_rslope

41

1

1.115876

EWYKT

Ts_ay

42

1.115708

EWYKT

Rs_ayu

1

1.114130

EWYKT

re_rslope

47

1

1.113540

EWYKT

re_rslope

35

1

1.113118

EWYKT

Rs_ayu

17

1.110713

NG

mu_beta2_pH

1

1.127960

NSEI

pH

45

2

2

1.140680

NSEI

Ry_ayu

8

1.111268

NSEI

pH

46

2

2

1.111162

NSEO

beta2_pelagic

1.257367

PWSI

beta1_pH

2

1.232581

PWSI

tau_beta2_pelagic

1.154036

PWSI

beta1_pelagic

1.115275

PWSO

beta0_pelagic

1.274838

PWSO

Ro_ayg

5

1.243986

PWSO

beta1_pelagic

1.215965

PWSO

Ro_ayg

2

1.204293

PWSO

p_pelagic

2

1

1.115571

PWSO

p_pelagic

11

1

1.114696

PWSO

p_pelagic

5

1

1.113118

PWSO

p_pelagic

1

1

1.112834

PWSO

p_pelagic

3

1

1.111389

PWSO

p_pelagic

3

2

1.110212

PWSO

Ro_ayu

9

1.110046

SOKO2SAP

Ro_ayu

3

1.255592

SOKO2SAP

Ro_ayu

47

1.253107

SOKO2SAP

Ro_ay

3

1.251893

SOKO2SAP

Ro_ayu

1

1.243520

SOKO2SAP

Ro_ayu

8

1.243168

SOKO2SAP

Ro_ay

47

1.240081

SOKO2SAP

Ro_ayu

5

1.236644

SOKO2SAP

Ro_ay

8

1.235769

SOKO2SAP

Ro_ay

1

1.220581

SOKO2SAP

Ro_ayu

25

1.218198

SOKO2SAP

Ro_ay

5

1.212611

SOKO2SAP

Ro_ayu

46

1.207589

SOKO2SAP

Ry_ayg

6

1.201420

SOKO2SAP

Ro_ay

25

1.199972

SOKO2SAP

Ro_ay

46

1.198565

SOKO2SAP

Ro_ayu

18

1.194459

SOKO2SAP

Ro_ayu

19

1.189236

SOKO2SAP

Ro_ayu

16

1.188869

SOKO2SAP

Hy_ayg

6

1.181072

SOKO2SAP

Ro_ay

19

1.173945

SOKO2SAP

H_ayg

6

1.173242

SOKO2SAP

Ro_ay

18

1.172665

SOKO2SAP

Ro_ay

16

1.169390

SOKO2SAP

Ro_ayu

24

1.162121

SOKO2SAP

Ro_ayu

44

1.158357

SOKO2SAP

Ro_ay

24

1.153460

SOKO2SAP

Hb_ayg

6

1.152811

SOKO2SAP

Hp_ayg

6

1.152752

SOKO2SAP

Ro_ay

44

1.147860

SOKO2SAP

Ro_ayu

7

1.146223

SOKO2SAP

Ro_ayu

40

1.141281

SOKO2SAP

Ro_ayu

43

1.140363

SOKO2SAP

Ro_ay

7

1.140168

SOKO2SAP

Ro_ayu

30

1.139692

SOKO2SAP

Ry_ay

6

1.139228

SOKO2SAP

Ro_ay

30

1.139094

SOKO2SAP

beta1_pH

3

1.138702

SOKO2SAP

Ho_ayg

6

1.138567

SOKO2SAP

Ro_ay

43

1.135536

SOKO2SAP

Ry_ayu

6

1.134419

SOKO2SAP

Ry_ayg

2

1.134177

SOKO2SAP

Ro_ayu

4

1.130091

SOKO2SAP

Ro_ay

40

1.129357

SOKO2SAP

Ro_ay

4

1.127163

SOKO2SAP

Ro_ayu

11

1.126849

SOKO2SAP

Ro_ayu

9

1.122326

SOKO2SAP

Ro_ayu

27

1.118878

SOKO2SAP

Ro_ay

27

1.118291

SOKO2SAP

Ry_ayg

8

1.117836

SOKO2SAP

Ro_ayu

15

1.111995

SOKO2SAP

Ry_ayg

10

1.111161

SOKO2SAP

Ro_ayu

10

1.110700

SSEI

pH

47

2

2

1.249959

SSEI

pH

45

2

2

1.246469

SSEI

pH

44

2

2

1.232596

SSEI

Ry_ayu

6

1.124609

SSEI

Ry_ay

6

1.120169

SSEO

Rdnye_ayu

1

1.181875

SSEO

Ro_ayu

1

1.180764

SSEO

pH

46

2

2

1.162591

SSEO

Rs_ayu

1

1.145839

SSEO

pH

45

2

2

1.125200

WKMA

beta2_pH

1

1.293236

WKMA

Ro_ayu

11

1.200723

WKMA

Ro_ay

11

1.180526

WKMA

Ro_ayu

5

1.174916

WKMA

Ro_ay

5

1.165290

WKMA

R_ayu

11

1.120071

WKMA

Ro_ayu

10

1.113120

WKMA

R_ayu

5

1.110010

afognak

Ho_ayu

4

1.198469

afognak

Ro_ayu

3

1.168335

afognak

Ro_ayu

42

1.153694

afognak

Ro_ay

42

1.152346

afognak

Ro_ay

3

1.152248

afognak

Ro_ayu

8

1.117923

eastside

Ro_ayu

1

1.214232

eastside

Ro_ayu

2

1.168306

eastside

Ro_ayg

12

1.161034

eastside

Ro_ayu

5

1.147660

eastside

Hy_ayu

13

1.138569

eastside

Hy_ayu

1

1.132534

eastside

R_ayu

1

1.126226

eastside

Ro_ay

1

1.118540

eastside

Ro_ayu

11

1.116681

eastside

Ro_ayu

7

1.115505

eastside

beta4_pelagic

1.112558

northeast

Ro_ayg

2

1.139528

tau_beta0_slope

1.428344

tau_beta2_slope

1.116186

mu_beta0_slope

1.112874

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.127 0.074 -0.265 -0.129 0.032
mu_bc_H[2] -0.096 0.045 -0.174 -0.100 0.002
mu_bc_H[3] -0.437 0.070 -0.567 -0.439 -0.300
mu_bc_H[4] -0.989 0.190 -1.371 -0.985 -0.633
mu_bc_H[5] 0.951 1.026 -0.160 0.747 3.334
mu_bc_H[6] -2.143 0.318 -2.762 -2.147 -1.516
mu_bc_H[7] -0.464 0.114 -0.700 -0.459 -0.254
mu_bc_H[8] 0.238 0.359 -0.356 0.201 1.035
mu_bc_H[9] -0.296 0.136 -0.570 -0.297 -0.021
mu_bc_H[10] -0.104 0.071 -0.234 -0.107 0.051
mu_bc_H[11] -0.122 0.038 -0.195 -0.123 -0.045
mu_bc_H[12] -0.256 0.109 -0.482 -0.252 -0.049
mu_bc_H[13] -0.141 0.079 -0.293 -0.142 0.017
mu_bc_H[14] -0.311 0.099 -0.501 -0.309 -0.119
mu_bc_H[15] -0.344 0.051 -0.448 -0.343 -0.245
mu_bc_H[16] -0.282 0.380 -0.910 -0.315 0.549
mu_bc_R[1] 1.349 0.149 1.058 1.346 1.640
mu_bc_R[2] 1.466 0.091 1.287 1.470 1.641
mu_bc_R[3] 1.391 0.144 1.106 1.392 1.677
mu_bc_R[4] 0.914 0.202 0.481 0.923 1.292
mu_bc_R[5] 1.179 0.460 0.303 1.180 2.069
mu_bc_R[6] -1.564 0.440 -2.414 -1.566 -0.698
mu_bc_R[7] 0.495 0.214 0.050 0.502 0.893
mu_bc_R[8] 0.480 0.181 0.123 0.477 0.841
mu_bc_R[9] 0.311 0.188 -0.086 0.324 0.650
mu_bc_R[10] 1.385 0.162 1.052 1.392 1.677
mu_bc_R[11] 1.051 0.097 0.862 1.050 1.250
mu_bc_R[12] 0.849 0.198 0.457 0.851 1.227
mu_bc_R[13] 1.053 0.099 0.854 1.055 1.243
mu_bc_R[14] 0.911 0.141 0.638 0.910 1.190
mu_bc_R[15] 0.826 0.110 0.610 0.825 1.038
mu_bc_R[16] 1.142 0.126 0.889 1.142 1.381
tau_pH[1] 5.186 0.449 4.354 5.171 6.079
tau_pH[2] 2.047 0.232 1.596 2.039 2.522
tau_pH[3] 2.128 0.217 1.724 2.120 2.590
beta0_pH[1,1] 0.534 0.176 0.172 0.536 0.868
beta0_pH[2,1] 1.305 0.191 0.912 1.309 1.675
beta0_pH[3,1] 1.388 0.209 0.915 1.406 1.754
beta0_pH[4,1] 1.551 0.228 1.022 1.564 1.939
beta0_pH[5,1] -0.862 0.278 -1.468 -0.843 -0.371
beta0_pH[6,1] -0.742 0.460 -1.870 -0.661 -0.082
beta0_pH[7,1] -0.485 0.501 -1.532 -0.461 0.494
beta0_pH[8,1] -0.710 0.307 -1.355 -0.672 -0.215
beta0_pH[9,1] -0.675 0.285 -1.301 -0.657 -0.194
beta0_pH[10,1] 0.312 0.198 -0.102 0.321 0.685
beta0_pH[11,1] -0.093 0.162 -0.428 -0.090 0.222
beta0_pH[12,1] 0.456 0.193 0.079 0.459 0.824
beta0_pH[13,1] -0.025 0.145 -0.322 -0.025 0.254
beta0_pH[14,1] -0.335 0.164 -0.662 -0.333 -0.019
beta0_pH[15,1] -0.103 0.185 -0.493 -0.096 0.234
beta0_pH[16,1] -0.502 0.365 -1.405 -0.435 0.026
beta0_pH[1,2] 2.836 0.162 2.511 2.838 3.150
beta0_pH[2,2] 2.892 0.133 2.627 2.894 3.153
beta0_pH[3,2] 3.129 0.158 2.838 3.128 3.421
beta0_pH[4,2] 2.948 0.129 2.701 2.948 3.201
beta0_pH[5,2] 4.941 1.447 3.070 4.641 8.732
beta0_pH[6,2] 3.095 0.208 2.689 3.095 3.509
beta0_pH[7,2] 1.836 0.189 1.467 1.837 2.204
beta0_pH[8,2] 2.928 0.172 2.584 2.928 3.261
beta0_pH[9,2] 3.445 0.219 3.010 3.440 3.874
beta0_pH[10,2] 3.639 0.205 3.247 3.636 4.063
beta0_pH[11,2] -4.807 0.297 -5.424 -4.803 -4.232
beta0_pH[12,2] -4.749 0.382 -5.509 -4.743 -3.994
beta0_pH[13,2] -4.549 0.393 -5.313 -4.560 -3.743
beta0_pH[14,2] -5.557 0.474 -6.516 -5.528 -4.712
beta0_pH[15,2] -4.259 0.333 -4.901 -4.252 -3.607
beta0_pH[16,2] -4.816 0.383 -5.595 -4.812 -4.099
beta0_pH[1,3] -0.080 0.717 -1.756 0.000 1.064
beta0_pH[2,3] 2.199 0.165 1.876 2.203 2.525
beta0_pH[3,3] 2.529 0.153 2.235 2.530 2.833
beta0_pH[4,3] 2.975 0.161 2.667 2.974 3.293
beta0_pH[5,3] 2.086 1.303 0.372 1.831 5.281
beta0_pH[6,3] 1.001 0.493 -0.173 1.030 1.855
beta0_pH[7,3] 0.623 0.173 0.292 0.621 0.980
beta0_pH[8,3] 0.301 0.196 -0.083 0.302 0.695
beta0_pH[9,3] -0.681 0.419 -1.729 -0.630 0.032
beta0_pH[10,3] 0.415 0.434 -0.694 0.490 1.087
beta0_pH[11,3] -0.183 0.333 -0.822 -0.190 0.474
beta0_pH[12,3] -0.889 0.361 -1.647 -0.858 -0.260
beta0_pH[13,3] -0.141 0.321 -0.776 -0.147 0.497
beta0_pH[14,3] -0.289 0.269 -0.806 -0.297 0.248
beta0_pH[15,3] -0.718 0.294 -1.322 -0.704 -0.187
beta0_pH[16,3] -0.410 0.284 -0.977 -0.414 0.146
beta1_pH[1,1] 3.101 0.316 2.537 3.077 3.773
beta1_pH[2,1] 2.218 0.300 1.714 2.192 2.883
beta1_pH[3,1] 2.032 0.334 1.491 1.994 2.795
beta1_pH[4,1] 2.409 0.356 1.836 2.362 3.297
beta1_pH[5,1] 2.292 0.339 1.714 2.262 3.076
beta1_pH[6,1] 3.927 1.130 2.375 3.705 6.734
beta1_pH[7,1] 2.569 0.982 0.755 2.508 4.641
beta1_pH[8,1] 4.182 1.083 2.691 3.981 6.848
beta1_pH[9,1] 2.364 0.394 1.742 2.313 3.260
beta1_pH[10,1] 2.295 0.275 1.788 2.283 2.870
beta1_pH[11,1] 3.275 0.204 2.878 3.276 3.692
beta1_pH[12,1] 2.591 0.224 2.156 2.591 3.031
beta1_pH[13,1] 3.006 0.211 2.607 2.999 3.439
beta1_pH[14,1] 3.442 0.215 3.037 3.438 3.867
beta1_pH[15,1] 2.614 0.232 2.165 2.610 3.076
beta1_pH[16,1] 4.074 0.649 3.175 3.941 5.759
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.012 0.108 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.001 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.651 0.328 6.018 6.641 7.323
beta1_pH[12,2] 6.389 0.428 5.578 6.379 7.249
beta1_pH[13,2] 6.922 0.420 6.091 6.920 7.743
beta1_pH[14,2] 7.203 0.496 6.330 7.193 8.205
beta1_pH[15,2] 6.735 0.365 6.015 6.731 7.430
beta1_pH[16,2] 7.400 0.419 6.614 7.389 8.236
beta1_pH[1,3] 4.538 1.611 2.044 4.295 8.031
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 4.112 8.884 0.923 2.834 16.496
beta1_pH[6,3] 3.355 6.644 0.490 2.674 9.651
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.767 0.351 2.078 2.768 3.453
beta1_pH[9,3] 2.805 0.487 2.006 2.754 4.015
beta1_pH[10,3] 2.965 0.507 2.165 2.893 4.176
beta1_pH[11,3] 2.777 0.390 2.016 2.773 3.544
beta1_pH[12,3] 4.158 0.449 3.322 4.130 5.110
beta1_pH[13,3] 1.729 0.344 1.055 1.726 2.413
beta1_pH[14,3] 2.534 0.347 1.862 2.535 3.200
beta1_pH[15,3] 2.000 0.322 1.401 1.994 2.675
beta1_pH[16,3] 1.815 0.314 1.184 1.811 2.435
beta2_pH[1,1] 0.478 0.122 0.289 0.465 0.745
beta2_pH[2,1] 0.573 0.298 0.242 0.513 1.287
beta2_pH[3,1] 0.621 0.438 0.213 0.534 1.576
beta2_pH[4,1] 0.468 0.182 0.199 0.438 0.922
beta2_pH[5,1] 1.447 0.995 0.244 1.303 3.753
beta2_pH[6,1] 0.178 0.062 0.088 0.168 0.322
beta2_pH[7,1] 0.232 4.513 0.000 0.000 0.284
beta2_pH[8,1] 0.237 0.095 0.121 0.217 0.460
beta2_pH[9,1] 0.424 0.195 0.175 0.391 0.889
beta2_pH[10,1] 0.600 0.256 0.288 0.553 1.237
beta2_pH[11,1] 0.794 0.226 0.483 0.757 1.317
beta2_pH[12,1] 1.321 0.467 0.746 1.217 2.534
beta2_pH[13,1] 0.727 0.207 0.416 0.701 1.226
beta2_pH[14,1] 0.828 0.203 0.528 0.798 1.325
beta2_pH[15,1] 0.778 0.286 0.398 0.728 1.472
beta2_pH[16,1] 0.407 0.182 0.176 0.360 0.851
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -2.027 1.881 -6.994 -1.511 -0.030
beta2_pH[4,2] -2.037 1.798 -6.609 -1.583 -0.033
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.751 4.391 -20.432 -8.738 -4.177
beta2_pH[12,2] -8.462 4.980 -20.004 -7.533 -1.332
beta2_pH[13,2] -8.216 5.067 -20.299 -7.207 -1.840
beta2_pH[14,2] -8.819 4.812 -20.580 -7.763 -2.450
beta2_pH[15,2] -9.552 4.473 -20.925 -8.553 -3.910
beta2_pH[16,2] -9.795 4.427 -20.805 -8.824 -4.185
beta2_pH[1,3] 0.255 0.387 0.101 0.185 0.709
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.343 6.372 -0.414 7.520 23.207
beta2_pH[6,3] 8.515 6.198 0.140 7.564 22.927
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 9.541 5.622 1.575 8.453 22.971
beta2_pH[9,3] 8.320 6.272 0.440 7.295 22.991
beta2_pH[10,3] 7.771 6.423 0.447 6.766 22.744
beta2_pH[11,3] -2.422 2.871 -9.050 -1.704 -0.616
beta2_pH[12,3] -2.592 2.680 -9.619 -1.868 -0.930
beta2_pH[13,3] -3.035 3.092 -10.428 -2.152 -0.796
beta2_pH[14,3] -3.016 3.000 -10.945 -2.134 -0.884
beta2_pH[15,3] -3.185 3.060 -11.321 -2.247 -1.025
beta2_pH[16,3] -3.179 3.042 -10.749 -2.261 -0.864
beta3_pH[1,1] 35.904 0.832 34.288 35.876 37.575
beta3_pH[2,1] 33.323 1.193 31.318 33.219 36.022
beta3_pH[3,1] 33.539 1.128 31.356 33.510 35.921
beta3_pH[4,1] 33.798 1.202 31.590 33.744 36.217
beta3_pH[5,1] 27.701 1.057 26.478 27.459 30.823
beta3_pH[6,1] 38.461 3.284 32.346 38.271 44.940
beta3_pH[7,1] 30.910 7.935 18.565 30.186 45.060
beta3_pH[8,1] 40.109 2.205 36.266 39.846 45.084
beta3_pH[9,1] 30.621 1.479 28.035 30.490 33.890
beta3_pH[10,1] 32.988 0.969 31.199 32.944 34.963
beta3_pH[11,1] 30.318 0.461 29.386 30.316 31.214
beta3_pH[12,1] 30.151 0.406 29.312 30.164 30.914
beta3_pH[13,1] 33.105 0.592 31.964 33.077 34.298
beta3_pH[14,1] 32.012 0.457 31.156 31.999 32.960
beta3_pH[15,1] 31.037 0.648 29.724 31.038 32.280
beta3_pH[16,1] 31.792 0.984 30.133 31.681 34.133
beta3_pH[1,2] 30.022 7.999 18.497 29.008 44.947
beta3_pH[2,2] 30.138 7.996 18.443 29.187 44.903
beta3_pH[3,2] 30.142 8.024 18.486 29.166 44.798
beta3_pH[4,2] 30.051 7.950 18.550 28.930 44.926
beta3_pH[5,2] 29.956 7.911 18.416 29.173 44.835
beta3_pH[6,2] 29.966 7.929 18.454 28.950 45.118
beta3_pH[7,2] 30.082 7.985 18.483 28.994 45.093
beta3_pH[8,2] 29.871 7.893 18.459 28.740 44.819
beta3_pH[9,2] 29.843 8.031 18.493 28.851 44.942
beta3_pH[10,2] 30.010 7.977 18.476 29.296 44.958
beta3_pH[11,2] 43.409 0.184 43.115 43.386 43.789
beta3_pH[12,2] 43.198 0.189 42.973 43.148 43.714
beta3_pH[13,2] 43.882 0.133 43.542 43.916 44.037
beta3_pH[14,2] 43.304 0.209 43.046 43.249 43.818
beta3_pH[15,2] 43.410 0.192 43.104 43.388 43.800
beta3_pH[16,2] 43.508 0.185 43.167 43.508 43.854
beta3_pH[1,3] 39.078 3.282 32.538 39.039 45.189
beta3_pH[2,3] 30.345 7.945 18.491 29.540 45.042
beta3_pH[3,3] 30.585 7.957 18.499 29.937 45.142
beta3_pH[4,3] 30.323 7.985 18.553 29.572 44.953
beta3_pH[5,3] 36.615 3.856 31.218 36.063 45.029
beta3_pH[6,3] 40.489 3.468 32.035 40.768 45.626
beta3_pH[7,3] 37.985 4.322 31.294 37.777 45.554
beta3_pH[8,3] 41.490 0.256 41.048 41.496 41.926
beta3_pH[9,3] 33.406 0.649 31.437 33.515 34.332
beta3_pH[10,3] 35.682 0.922 33.183 35.974 36.847
beta3_pH[11,3] 41.791 0.802 40.179 41.806 43.333
beta3_pH[12,3] 41.719 0.387 40.962 41.731 42.485
beta3_pH[13,3] 42.766 0.870 41.105 42.782 44.729
beta3_pH[14,3] 41.109 0.587 39.880 41.126 42.178
beta3_pH[15,3] 42.594 0.654 41.189 42.656 43.745
beta3_pH[16,3] 42.882 0.746 41.120 42.995 44.099
beta4_pH[1,1] 2.190 3.471 -0.005 1.167 12.721
beta4_pH[2,1] 2.680 3.561 0.125 1.452 13.499
beta4_pH[3,1] 1.799 3.722 -1.006 0.682 13.457
beta4_pH[4,1] 2.277 3.734 -1.192 1.137 13.020
beta4_pH[5,1] -0.637 0.685 -2.098 -0.584 0.520
beta4_pH[6,1] -0.577 0.698 -2.034 -0.549 0.672
beta4_pH[7,1] 0.953 2.012 -1.659 0.433 6.684
beta4_pH[8,1] 0.822 1.861 -1.251 0.277 6.250
beta4_pH[9,1] 1.232 1.958 -1.164 0.700 6.195
beta4_pH[10,1] 1.489 1.883 -0.418 0.873 6.929
beta4_pH[11,1] 6.336 6.011 -0.724 4.752 21.150
beta4_pH[12,1] 6.580 5.939 -0.534 4.983 20.688
beta4_pH[13,1] 6.936 5.656 0.433 5.319 21.273
beta4_pH[14,1] 7.021 5.545 0.528 5.475 21.144
beta4_pH[15,1] 6.059 6.217 -0.965 4.425 21.117
beta4_pH[16,1] 6.292 6.042 -0.797 4.745 20.857
beta4_pH[1,2] -2.603 3.203 -3.956 -3.418 8.681
beta4_pH[2,2] 0.676 3.286 -2.082 -0.405 9.824
beta4_pH[3,2] -0.779 3.469 -3.460 -2.025 8.984
beta4_pH[4,2] 1.797 2.983 -1.132 0.961 9.783
beta4_pH[5,2] -3.039 2.065 -3.998 -3.637 1.031
beta4_pH[6,2] -3.203 1.893 -3.997 -3.731 0.602
beta4_pH[7,2] -0.023 0.957 -1.816 -0.058 1.890
beta4_pH[8,2] -2.999 1.854 -3.998 -3.367 -0.175
beta4_pH[9,2] -3.133 1.998 -3.998 -3.680 0.484
beta4_pH[10,2] -3.609 1.814 -3.998 -3.891 -2.256
beta4_pH[11,2] -0.698 0.490 -1.478 -0.750 0.344
beta4_pH[12,2] -1.541 0.775 -2.699 -1.633 0.281
beta4_pH[13,2] -1.998 0.708 -3.072 -2.099 -0.326
beta4_pH[14,2] -0.464 0.878 -1.601 -0.637 1.642
beta4_pH[15,2] -2.161 0.655 -3.184 -2.231 -0.705
beta4_pH[16,2] -1.398 0.786 -2.491 -1.526 0.540
beta4_pH[1,3] -0.667 1.810 -2.620 -1.148 4.334
beta4_pH[2,3] -1.269 1.162 -2.246 -1.469 0.791
beta4_pH[3,3] -1.618 1.261 -2.788 -1.825 0.827
beta4_pH[4,3] -0.503 1.648 -2.080 -0.993 4.405
beta4_pH[5,3] 6.424 6.610 -2.382 5.142 22.242
beta4_pH[6,3] 6.489 6.631 -2.083 5.033 22.124
beta4_pH[7,3] 6.315 6.600 -2.080 4.965 22.162
beta4_pH[8,3] 6.626 6.407 -1.261 5.126 22.208
beta4_pH[9,3] 6.609 6.373 -1.213 5.091 21.487
beta4_pH[10,3] 6.170 6.746 -2.031 4.775 22.174
beta4_pH[11,3] 2.162 3.196 -0.423 1.154 11.421
beta4_pH[12,3] 2.008 3.389 -0.799 0.978 11.702
beta4_pH[13,3] 1.139 3.305 -0.858 0.201 11.362
beta4_pH[14,3] 1.608 3.317 -0.913 0.575 11.587
beta4_pH[15,3] 1.077 3.048 -0.693 0.249 11.229
beta4_pH[16,3] 1.821 3.254 -0.497 0.775 11.676
beta0_pelagic[1] 2.228 0.128 1.975 2.227 2.488
beta0_pelagic[2] 1.515 0.127 1.258 1.517 1.763
beta0_pelagic[3] -0.408 0.803 -2.240 -0.174 0.621
beta0_pelagic[4] -0.487 1.111 -3.834 -0.159 0.774
beta0_pelagic[5] 1.181 0.252 0.673 1.181 1.674
beta0_pelagic[6] 1.461 0.269 0.912 1.477 1.963
beta0_pelagic[7] 1.597 0.210 1.192 1.589 2.033
beta0_pelagic[8] 1.758 0.203 1.349 1.754 2.187
beta0_pelagic[9] 2.487 0.316 1.883 2.489 3.081
beta0_pelagic[10] 2.506 0.211 2.053 2.515 2.899
beta0_pelagic[11] 0.310 0.355 -0.589 0.416 0.781
beta0_pelagic[12] 1.677 0.141 1.399 1.680 1.945
beta0_pelagic[13] 0.330 0.200 -0.096 0.344 0.668
beta0_pelagic[14] -0.063 0.276 -0.697 -0.038 0.397
beta0_pelagic[15] -0.255 0.139 -0.528 -0.254 0.020
beta0_pelagic[16] 0.331 0.251 -0.344 0.378 0.686
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 2.009 1.351 0.460 1.593 5.441
beta1_pelagic[4] 1.907 1.270 0.424 1.534 5.363
beta1_pelagic[5] -0.074 0.319 -0.700 -0.073 0.572
beta1_pelagic[6] -0.095 0.442 -0.835 -0.155 0.723
beta1_pelagic[7] -0.020 0.288 -0.578 -0.018 0.553
beta1_pelagic[8] -0.014 0.280 -0.558 -0.015 0.539
beta1_pelagic[9] 0.194 0.495 -0.777 0.309 0.955
beta1_pelagic[10] 0.060 0.271 -0.474 0.059 0.589
beta1_pelagic[11] 3.115 0.949 2.034 2.779 5.820
beta1_pelagic[12] 2.703 0.325 2.099 2.697 3.346
beta1_pelagic[13] 2.814 0.736 1.674 2.704 4.559
beta1_pelagic[14] 4.174 1.067 2.719 3.918 6.719
beta1_pelagic[15] 2.897 0.270 2.409 2.891 3.427
beta1_pelagic[16] 3.450 0.835 2.642 3.223 6.237
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.834 2.635 0.031 0.159 8.619
beta2_pelagic[4] 1.429 3.360 0.032 0.367 13.268
beta2_pelagic[5] -0.020 0.655 -1.440 -0.021 1.319
beta2_pelagic[6] -0.090 0.681 -1.435 -0.137 1.309
beta2_pelagic[7] 0.012 0.648 -1.347 -0.004 1.411
beta2_pelagic[8] 0.013 0.625 -1.297 0.004 1.365
beta2_pelagic[9] 0.168 0.682 -1.303 0.239 1.468
beta2_pelagic[10] 0.016 0.631 -1.345 0.027 1.342
beta2_pelagic[11] 3.581 5.399 0.138 1.320 19.807
beta2_pelagic[12] 7.008 5.987 1.198 5.026 23.773
beta2_pelagic[13] 1.263 2.801 0.198 0.509 8.699
beta2_pelagic[14] 0.370 0.671 0.160 0.307 0.780
beta2_pelagic[15] 7.031 5.536 1.394 5.395 23.115
beta2_pelagic[16] 5.919 6.183 0.209 4.217 22.757
beta3_pelagic[1] 30.081 7.944 18.418 29.347 44.783
beta3_pelagic[2] 29.898 7.963 18.494 28.849 45.015
beta3_pelagic[3] 29.942 6.343 19.157 29.358 44.068
beta3_pelagic[4] 24.935 5.155 18.362 24.306 40.641
beta3_pelagic[5] 30.385 8.236 18.422 29.233 45.257
beta3_pelagic[6] 31.707 6.774 18.947 31.644 44.305
beta3_pelagic[7] 29.676 7.942 18.377 28.482 44.959
beta3_pelagic[8] 29.593 7.945 18.467 28.157 44.998
beta3_pelagic[9] 30.798 6.110 19.017 30.897 42.919
beta3_pelagic[10] 29.550 8.207 18.331 28.125 45.033
beta3_pelagic[11] 42.811 1.364 38.794 43.111 45.136
beta3_pelagic[12] 43.472 0.285 43.003 43.456 44.011
beta3_pelagic[13] 42.736 1.276 40.353 42.711 45.521
beta3_pelagic[14] 42.276 1.676 38.862 42.232 45.531
beta3_pelagic[15] 43.207 0.250 42.680 43.196 43.702
beta3_pelagic[16] 43.152 0.709 41.361 43.222 44.616
mu_beta0_pelagic[1] 0.643 1.088 -1.704 0.746 2.693
mu_beta0_pelagic[2] 1.808 0.394 1.027 1.809 2.592
mu_beta0_pelagic[3] 0.381 0.434 -0.471 0.389 1.234
tau_beta0_pelagic[1] 0.468 0.557 0.047 0.285 2.010
tau_beta0_pelagic[2] 2.765 3.317 0.255 1.967 9.952
tau_beta0_pelagic[3] 1.656 1.216 0.196 1.360 4.752
beta0_yellow[1] -0.535 0.195 -1.009 -0.521 -0.206
beta0_yellow[2] 0.500 0.177 0.155 0.510 0.795
beta0_yellow[3] -0.333 0.187 -0.745 -0.319 0.005
beta0_yellow[4] 0.827 0.355 0.048 0.885 1.223
beta0_yellow[5] -0.282 0.353 -0.955 -0.290 0.412
beta0_yellow[6] 1.115 0.164 0.793 1.115 1.441
beta0_yellow[7] 0.990 0.161 0.675 0.987 1.305
beta0_yellow[8] 1.017 0.153 0.714 1.016 1.317
beta0_yellow[9] 0.656 0.155 0.354 0.661 0.959
beta0_yellow[10] 0.582 0.142 0.299 0.584 0.846
beta0_yellow[11] -1.963 0.460 -2.861 -1.975 -1.032
beta0_yellow[12] -3.832 0.473 -4.877 -3.799 -3.018
beta0_yellow[13] -3.801 0.503 -4.893 -3.762 -2.925
beta0_yellow[14] -2.094 0.568 -3.074 -2.141 -0.701
beta0_yellow[15] -2.867 0.438 -3.744 -2.849 -2.056
beta0_yellow[16] -2.426 0.491 -3.391 -2.413 -1.478
beta1_yellow[1] 0.917 1.510 0.010 0.687 3.256
beta1_yellow[2] 1.085 0.417 0.579 1.023 2.075
beta1_yellow[3] 0.721 0.278 0.272 0.707 1.305
beta1_yellow[4] 1.369 0.830 0.635 1.168 3.867
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.116 0.458 1.181 2.108 3.051
beta1_yellow[12] 2.626 0.487 1.790 2.590 3.688
beta1_yellow[13] 2.914 0.510 2.050 2.879 4.032
beta1_yellow[14] 2.176 0.545 0.921 2.191 3.180
beta1_yellow[15] 2.116 0.434 1.323 2.096 3.013
beta1_yellow[16] 2.184 0.494 1.198 2.182 3.141
beta2_yellow[1] -3.972 3.645 -13.988 -2.907 -0.082
beta2_yellow[2] -3.673 3.188 -11.653 -2.708 -0.170
beta2_yellow[3] -3.660 3.318 -12.330 -2.733 -0.152
beta2_yellow[4] -3.228 3.258 -11.720 -2.176 -0.099
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.786 2.881 -11.467 -4.003 -0.982
beta2_yellow[12] -5.106 2.869 -12.296 -4.429 -1.536
beta2_yellow[13] -4.887 2.634 -11.518 -4.267 -1.509
beta2_yellow[14] -4.808 2.937 -11.650 -4.261 -0.495
beta2_yellow[15] -4.520 2.884 -11.443 -3.758 -1.019
beta2_yellow[16] -5.170 2.881 -12.241 -4.569 -1.357
beta3_yellow[1] 25.665 7.125 18.274 22.549 44.273
beta3_yellow[2] 29.057 2.008 24.331 28.899 32.939
beta3_yellow[3] 33.066 2.989 26.308 32.938 39.411
beta3_yellow[4] 29.138 3.455 22.491 28.103 36.236
beta3_yellow[5] 29.853 7.916 18.559 28.855 44.881
beta3_yellow[6] 30.213 8.025 18.437 29.546 44.861
beta3_yellow[7] 29.891 7.935 18.572 28.860 44.770
beta3_yellow[8] 30.013 7.928 18.377 28.925 44.758
beta3_yellow[9] 29.822 7.819 18.562 28.895 44.874
beta3_yellow[10] 30.023 7.913 18.476 29.326 44.907
beta3_yellow[11] 45.283 0.701 43.995 45.385 45.974
beta3_yellow[12] 43.307 0.350 42.609 43.285 43.995
beta3_yellow[13] 44.890 0.386 44.022 44.959 45.557
beta3_yellow[14] 44.011 1.811 36.437 44.224 45.853
beta3_yellow[15] 45.165 0.592 44.141 45.162 45.974
beta3_yellow[16] 44.549 0.670 43.391 44.537 45.816
mu_beta0_yellow[1] 0.097 0.548 -1.011 0.093 1.250
mu_beta0_yellow[2] 0.648 0.336 -0.111 0.670 1.269
mu_beta0_yellow[3] -2.442 0.692 -3.542 -2.552 -0.681
tau_beta0_yellow[1] 1.852 2.890 0.095 1.174 7.367
tau_beta0_yellow[2] 3.747 4.971 0.301 2.406 15.346
tau_beta0_yellow[3] 1.300 1.871 0.085 0.763 5.297
beta0_black[1] -0.078 0.159 -0.388 -0.076 0.230
beta0_black[2] 1.913 0.128 1.661 1.912 2.165
beta0_black[3] 1.321 0.134 1.068 1.319 1.585
beta0_black[4] 2.426 0.136 2.165 2.425 2.698
beta0_black[5] 4.660 2.094 1.785 4.241 9.768
beta0_black[6] 4.590 1.906 2.241 4.112 9.512
beta0_black[7] 3.720 1.847 1.555 3.252 8.434
beta0_black[8] 0.954 0.211 0.547 0.953 1.368
beta0_black[9] 2.598 0.232 2.143 2.597 3.065
beta0_black[10] 1.460 0.133 1.199 1.461 1.723
beta0_black[11] 3.487 0.155 3.186 3.489 3.789
beta0_black[12] 4.865 0.171 4.531 4.866 5.200
beta0_black[13] -0.116 0.243 -0.614 -0.106 0.318
beta0_black[14] 2.849 0.157 2.546 2.853 3.165
beta0_black[15] 1.290 0.157 0.989 1.288 1.605
beta0_black[16] 4.272 0.161 3.952 4.272 4.583
beta2_black[1] 7.520 9.810 0.497 3.397 38.849
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.217 1.805 -7.359 -1.646 -0.438
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.715 1.422 39.673 41.949 43.325
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.268 0.829 37.537 39.354 40.611
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.265 0.193 -0.632 -0.269 0.118
beta4_black[2] 0.247 0.186 -0.126 0.245 0.610
beta4_black[3] -0.940 0.196 -1.332 -0.937 -0.563
beta4_black[4] 0.425 0.218 0.003 0.420 0.868
beta4_black[5] 0.514 1.254 -1.345 0.335 3.655
beta4_black[6] 0.544 1.249 -1.326 0.342 3.562
beta4_black[7] 0.448 1.179 -1.350 0.257 3.464
beta4_black[8] -0.242 0.317 -0.884 -0.236 0.355
beta4_black[9] 0.863 0.782 -0.222 0.704 2.798
beta4_black[10] 0.045 0.183 -0.314 0.042 0.407
beta4_black[11] -0.697 0.213 -1.112 -0.696 -0.277
beta4_black[12] 0.175 0.324 -0.437 0.164 0.842
beta4_black[13] -1.185 0.222 -1.620 -1.194 -0.745
beta4_black[14] -0.177 0.238 -0.621 -0.179 0.293
beta4_black[15] -0.887 0.215 -1.296 -0.884 -0.479
beta4_black[16] -0.590 0.230 -1.046 -0.596 -0.152
mu_beta0_black[1] 1.276 0.898 -0.657 1.307 3.048
mu_beta0_black[2] 2.699 1.054 0.779 2.586 5.057
mu_beta0_black[3] 2.496 1.016 0.213 2.538 4.375
tau_beta0_black[1] 0.634 0.594 0.059 0.447 2.181
tau_beta0_black[2] 0.459 0.680 0.046 0.246 2.077
tau_beta0_black[3] 0.232 0.158 0.049 0.192 0.636
beta0_dsr[11] -2.902 0.286 -3.475 -2.903 -2.350
beta0_dsr[12] 4.572 0.278 4.035 4.567 5.122
beta0_dsr[13] -1.384 0.382 -2.032 -1.359 -0.802
beta0_dsr[14] -3.662 0.513 -4.681 -3.650 -2.636
beta0_dsr[15] -1.940 0.285 -2.502 -1.944 -1.390
beta0_dsr[16] -2.975 0.375 -3.719 -2.963 -2.234
beta1_dsr[11] 4.839 0.299 4.269 4.838 5.458
beta1_dsr[12] 6.593 15.356 2.269 4.941 18.677
beta1_dsr[13] 2.905 0.473 2.283 2.864 3.692
beta1_dsr[14] 6.329 0.540 5.269 6.321 7.415
beta1_dsr[15] 3.344 0.289 2.788 3.343 3.925
beta1_dsr[16] 5.791 0.393 5.033 5.786 6.574
beta2_dsr[11] -8.209 2.295 -13.509 -7.881 -4.644
beta2_dsr[12] -7.071 2.632 -13.048 -6.900 -2.390
beta2_dsr[13] -6.366 2.849 -12.854 -6.265 -0.567
beta2_dsr[14] -6.128 2.759 -11.997 -6.015 -1.689
beta2_dsr[15] -7.655 2.406 -13.174 -7.293 -3.861
beta2_dsr[16] -7.901 2.320 -13.374 -7.548 -4.238
beta3_dsr[11] 43.491 0.151 43.215 43.488 43.783
beta3_dsr[12] 33.970 0.742 32.140 34.125 34.825
beta3_dsr[13] 43.251 0.378 42.744 43.194 43.889
beta3_dsr[14] 43.355 0.248 43.073 43.277 43.981
beta3_dsr[15] 43.505 0.185 43.166 43.505 43.851
beta3_dsr[16] 43.442 0.158 43.176 43.430 43.764
beta4_dsr[11] 0.587 0.224 0.156 0.583 1.029
beta4_dsr[12] 0.238 0.427 -0.585 0.222 1.092
beta4_dsr[13] -0.161 0.221 -0.603 -0.160 0.261
beta4_dsr[14] 0.148 0.248 -0.346 0.152 0.630
beta4_dsr[15] 0.715 0.216 0.295 0.714 1.139
beta4_dsr[16] 0.153 0.228 -0.296 0.156 0.594
beta0_slope[11] -1.846 0.147 -2.129 -1.850 -1.557
beta0_slope[12] -5.707 1.964 -10.087 -4.569 -4.031
beta0_slope[13] -1.333 0.158 -1.672 -1.324 -1.053
beta0_slope[14] -2.679 0.162 -2.988 -2.678 -2.359
beta0_slope[15] -1.341 0.143 -1.616 -1.339 -1.061
beta0_slope[16] -2.736 0.161 -3.056 -2.739 -2.421
beta1_slope[11] 4.487 0.217 4.062 4.489 4.909
beta1_slope[12] 4.085 0.797 2.810 4.002 6.103
beta1_slope[13] 2.703 0.363 2.232 2.665 3.500
beta1_slope[14] 6.340 0.403 5.572 6.336 7.164
beta1_slope[15] 3.003 0.206 2.604 3.000 3.397
beta1_slope[16] 5.244 0.275 4.710 5.243 5.789
beta2_slope[11] 8.812 2.374 5.176 8.459 14.631
beta2_slope[12] 7.145 2.804 1.688 6.992 13.030
beta2_slope[13] 5.670 3.017 0.575 5.616 11.920
beta2_slope[14] 6.579 2.584 2.304 6.472 12.291
beta2_slope[15] 8.343 2.378 4.485 8.071 13.947
beta2_slope[16] 7.931 2.278 4.246 7.631 13.168
beta3_slope[11] 43.461 0.133 43.230 43.454 43.723
beta3_slope[12] 40.365 4.273 33.931 43.198 43.867
beta3_slope[13] 43.454 0.358 42.966 43.402 44.007
beta3_slope[14] 43.260 0.135 43.091 43.226 43.597
beta3_slope[15] 43.489 0.161 43.198 43.488 43.790
beta3_slope[16] 43.367 0.144 43.148 43.347 43.698
beta4_slope[11] -0.726 0.163 -1.051 -0.726 -0.400
beta4_slope[12] -0.937 0.542 -2.043 -0.907 0.049
beta4_slope[13] 0.080 0.159 -0.231 0.082 0.391
beta4_slope[14] -0.088 0.192 -0.461 -0.092 0.300
beta4_slope[15] -0.760 0.157 -1.073 -0.759 -0.464
beta4_slope[16] -0.167 0.176 -0.500 -0.170 0.178
sigma_H[1] 0.202 0.054 0.104 0.200 0.320
sigma_H[2] 0.170 0.030 0.118 0.168 0.234
sigma_H[3] 0.196 0.043 0.119 0.193 0.285
sigma_H[4] 0.420 0.077 0.296 0.411 0.596
sigma_H[5] 0.996 0.208 0.609 0.986 1.425
sigma_H[6] 0.424 0.194 0.051 0.415 0.823
sigma_H[7] 0.307 0.063 0.209 0.299 0.453
sigma_H[8] 0.416 0.091 0.272 0.406 0.621
sigma_H[9] 0.531 0.126 0.332 0.514 0.815
sigma_H[10] 0.214 0.043 0.141 0.211 0.306
sigma_H[11] 0.278 0.047 0.200 0.272 0.378
sigma_H[12] 0.433 0.166 0.210 0.401 0.775
sigma_H[13] 0.215 0.037 0.150 0.211 0.293
sigma_H[14] 0.507 0.093 0.347 0.499 0.703
sigma_H[15] 0.248 0.040 0.182 0.244 0.337
sigma_H[16] 0.226 0.044 0.154 0.223 0.322
lambda_H[1] 3.287 4.439 0.155 1.853 14.438
lambda_H[2] 8.075 7.355 0.755 6.063 27.971
lambda_H[3] 6.528 9.819 0.257 3.351 31.789
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.613 8.058 0.033 0.995 24.882
lambda_H[6] 7.169 12.973 0.008 0.946 46.100
lambda_H[7] 0.013 0.009 0.002 0.010 0.036
lambda_H[8] 8.137 9.746 0.095 4.720 34.372
lambda_H[9] 0.015 0.010 0.003 0.013 0.041
lambda_H[10] 0.306 0.488 0.033 0.201 1.134
lambda_H[11] 0.278 0.475 0.010 0.133 1.233
lambda_H[12] 4.933 6.882 0.200 2.697 23.576
lambda_H[13] 3.599 3.197 0.262 2.715 12.186
lambda_H[14] 3.212 3.814 0.214 2.059 12.301
lambda_H[15] 0.027 0.046 0.004 0.017 0.108
lambda_H[16] 0.929 1.401 0.047 0.505 4.502
mu_lambda_H[1] 4.339 1.929 1.227 4.131 8.412
mu_lambda_H[2] 3.805 1.932 0.605 3.664 7.940
mu_lambda_H[3] 3.541 1.877 0.789 3.260 7.896
sigma_lambda_H[1] 8.555 4.351 2.053 7.894 18.218
sigma_lambda_H[2] 8.325 4.659 1.015 7.797 18.117
sigma_lambda_H[3] 6.351 4.056 1.072 5.415 16.586
beta_H[1,1] 6.944 1.048 4.453 7.112 8.552
beta_H[2,1] 9.873 0.490 8.807 9.896 10.776
beta_H[3,1] 8.014 0.813 6.124 8.106 9.335
beta_H[4,1] 9.342 7.929 -6.962 9.356 24.406
beta_H[5,1] 0.149 2.375 -4.841 0.292 4.047
beta_H[6,1] 3.053 4.013 -7.261 4.471 7.555
beta_H[7,1] 0.491 5.900 -12.426 0.927 10.977
beta_H[8,1] 1.502 4.505 -2.236 1.214 3.644
beta_H[9,1] 12.971 5.581 1.905 12.873 24.186
beta_H[10,1] 7.031 1.690 3.584 7.115 10.221
beta_H[11,1] 5.142 3.491 -2.674 5.959 9.923
beta_H[12,1] 2.613 1.050 0.763 2.547 4.959
beta_H[13,1] 9.045 0.925 7.188 9.126 10.494
beta_H[14,1] 2.200 1.058 0.179 2.201 4.218
beta_H[15,1] -5.975 3.844 -13.093 -6.180 2.432
beta_H[16,1] 3.321 2.485 -0.834 3.064 9.422
beta_H[1,2] 7.913 0.246 7.429 7.918 8.372
beta_H[2,2] 10.027 0.134 9.760 10.026 10.294
beta_H[3,2] 8.954 0.199 8.562 8.956 9.345
beta_H[4,2] 3.568 1.490 0.778 3.504 6.732
beta_H[5,2] 1.960 0.932 0.096 1.949 3.750
beta_H[6,2] 5.726 1.013 3.361 5.893 7.294
beta_H[7,2] 2.678 1.107 0.682 2.618 4.990
beta_H[8,2] 2.980 1.201 1.334 3.134 4.274
beta_H[9,2] 3.516 1.092 1.408 3.498 5.838
beta_H[10,2] 8.210 0.346 7.493 8.216 8.875
beta_H[11,2] 9.762 0.631 8.824 9.646 11.186
beta_H[12,2] 3.943 0.372 3.255 3.930 4.728
beta_H[13,2] 9.126 0.260 8.673 9.112 9.652
beta_H[14,2] 4.037 0.366 3.338 4.029 4.770
beta_H[15,2] 11.339 0.695 9.884 11.372 12.689
beta_H[16,2] 4.539 0.805 2.960 4.536 6.158
beta_H[1,3] 8.450 0.246 8.004 8.435 8.975
beta_H[2,3] 10.068 0.119 9.839 10.067 10.301
beta_H[3,3] 9.619 0.163 9.302 9.617 9.953
beta_H[4,3] -2.513 0.891 -4.347 -2.503 -0.810
beta_H[5,3] 3.838 0.599 2.611 3.836 4.965
beta_H[6,3] 7.932 1.186 6.349 7.555 10.491
beta_H[7,3] -2.779 0.662 -4.114 -2.754 -1.504
beta_H[8,3] 5.277 0.541 4.659 5.197 6.362
beta_H[9,3] -2.862 0.725 -4.335 -2.844 -1.451
beta_H[10,3] 8.677 0.273 8.145 8.679 9.215
beta_H[11,3] 8.532 0.284 7.888 8.558 9.025
beta_H[12,3] 5.259 0.324 4.487 5.297 5.796
beta_H[13,3] 8.854 0.176 8.503 8.863 9.195
beta_H[14,3] 5.723 0.285 5.099 5.746 6.222
beta_H[15,3] 10.379 0.317 9.775 10.379 11.001
beta_H[16,3] 6.339 0.574 5.072 6.396 7.298
beta_H[1,4] 8.270 0.182 7.868 8.284 8.583
beta_H[2,4] 10.132 0.118 9.880 10.140 10.342
beta_H[3,4] 10.118 0.161 9.761 10.133 10.398
beta_H[4,4] 11.796 0.449 10.935 11.787 12.675
beta_H[5,4] 5.493 0.759 4.289 5.415 7.226
beta_H[6,4] 7.005 0.944 4.910 7.294 8.292
beta_H[7,4] 8.288 0.349 7.611 8.280 8.951
beta_H[8,4] 6.703 0.267 6.237 6.717 7.134
beta_H[9,4] 7.220 0.479 6.304 7.208 8.150
beta_H[10,4] 7.749 0.235 7.305 7.745 8.234
beta_H[11,4] 9.388 0.199 8.997 9.390 9.773
beta_H[12,4] 7.154 0.220 6.748 7.142 7.617
beta_H[13,4] 9.053 0.140 8.771 9.056 9.319
beta_H[14,4] 7.747 0.223 7.314 7.743 8.199
beta_H[15,4] 9.476 0.234 9.027 9.471 9.928
beta_H[16,4] 9.327 0.234 8.903 9.316 9.823
beta_H[1,5] 8.989 0.146 8.690 8.989 9.266
beta_H[2,5] 10.782 0.095 10.597 10.782 10.970
beta_H[3,5] 10.919 0.171 10.613 10.912 11.264
beta_H[4,5] 8.377 0.462 7.473 8.370 9.312
beta_H[5,5] 5.423 0.583 4.040 5.468 6.416
beta_H[6,5] 8.821 0.645 7.880 8.670 10.361
beta_H[7,5] 6.752 0.333 6.106 6.744 7.423
beta_H[8,5] 8.217 0.222 7.850 8.202 8.624
beta_H[9,5] 8.196 0.481 7.218 8.203 9.126
beta_H[10,5] 10.088 0.225 9.635 10.090 10.532
beta_H[11,5] 11.510 0.233 11.044 11.509 11.965
beta_H[12,5] 8.483 0.198 8.108 8.481 8.893
beta_H[13,5] 10.009 0.130 9.755 10.008 10.256
beta_H[14,5] 9.206 0.229 8.780 9.196 9.694
beta_H[15,5] 11.157 0.247 10.675 11.151 11.639
beta_H[16,5] 9.922 0.176 9.566 9.929 10.265
beta_H[1,6] 10.171 0.185 9.838 10.164 10.582
beta_H[2,6] 11.510 0.108 11.293 11.513 11.717
beta_H[3,6] 10.815 0.160 10.469 10.827 11.097
beta_H[4,6] 12.887 0.817 11.234 12.908 14.453
beta_H[5,6] 5.918 0.618 4.723 5.908 7.157
beta_H[6,6] 8.788 0.706 6.900 8.925 9.779
beta_H[7,6] 9.873 0.574 8.752 9.871 11.015
beta_H[8,6] 9.502 0.300 8.933 9.528 9.945
beta_H[9,6] 8.471 0.800 6.938 8.459 10.115
beta_H[10,6] 9.508 0.319 8.806 9.536 10.067
beta_H[11,6] 10.807 0.354 10.037 10.826 11.430
beta_H[12,6] 9.380 0.248 8.905 9.373 9.903
beta_H[13,6] 11.045 0.162 10.754 11.040 11.381
beta_H[14,6] 9.839 0.290 9.249 9.845 10.390
beta_H[15,6] 10.855 0.432 10.001 10.849 11.733
beta_H[16,6] 10.548 0.232 10.051 10.561 10.984
beta_H[1,7] 10.895 0.856 8.784 10.995 12.311
beta_H[2,7] 12.211 0.431 11.366 12.219 13.046
beta_H[3,7] 10.557 0.676 9.103 10.622 11.668
beta_H[4,7] 2.462 4.195 -5.768 2.412 10.840
beta_H[5,7] 6.427 1.860 3.115 6.369 10.526
beta_H[6,7] 9.733 2.512 4.777 9.618 16.067
beta_H[7,7] 10.506 2.902 4.697 10.462 16.331
beta_H[8,7] 10.979 1.106 9.508 10.887 13.020
beta_H[9,7] 4.435 4.153 -4.011 4.505 12.465
beta_H[10,7] 9.797 1.482 7.188 9.690 13.227
beta_H[11,7] 10.991 1.712 7.875 10.885 14.866
beta_H[12,7] 9.969 0.925 7.879 10.058 11.520
beta_H[13,7] 11.685 0.736 9.926 11.774 12.797
beta_H[14,7] 10.450 0.952 8.463 10.497 12.144
beta_H[15,7] 11.976 2.242 7.462 11.993 16.193
beta_H[16,7] 12.225 1.215 10.189 12.073 15.006
beta0_H[1] 9.145 14.022 -17.349 8.869 35.800
beta0_H[2] 10.564 6.590 -2.884 10.590 23.852
beta0_H[3] 9.954 10.322 -10.635 9.973 30.781
beta0_H[4] 8.288 186.035 -370.309 10.183 377.506
beta0_H[5] 5.445 25.590 -42.836 4.493 54.915
beta0_H[6] 8.078 52.731 -105.161 7.587 117.058
beta0_H[7] 5.537 132.743 -273.364 7.491 273.742
beta0_H[8] 5.697 44.966 -17.470 6.537 29.254
beta0_H[9] 7.104 123.425 -234.183 7.708 262.691
beta0_H[10] 8.845 32.714 -56.310 8.281 75.981
beta0_H[11] 8.437 48.747 -97.911 9.420 107.543
beta0_H[12] 6.583 11.571 -16.187 6.558 27.656
beta0_H[13] 10.221 10.946 -9.106 9.919 30.251
beta0_H[14] 6.895 12.445 -17.324 6.809 29.265
beta0_H[15] 8.878 106.880 -210.661 7.974 231.956
beta0_H[16] 7.456 23.730 -41.595 7.472 54.993